anonymous
  • anonymous
Help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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campbell_st
  • campbell_st
well an easy method is to graph the curve... and look where a tangent to the curve would have a negative slope
campbell_st
  • campbell_st
the other is to use calculus to sketch the curve
ybarrap
  • ybarrap
You are looking for where f'(x) < 0 Take the first derivative and see where this occurs
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ybarrap
  • ybarrap
Here is f'(x) $$ f'(x)=(x-6) (x-2) $$ When is this negative?
anonymous
  • anonymous
At 6 and 2?
ybarrap
  • ybarrap
BETWEEN 6 and 2, right? |dw:1436130851705:dw|
ybarrap
  • ybarrap
|dw:1436130906919:dw|
ybarrap
  • ybarrap
$$ 2\lt x\lt 6 $$ Note that it does NOT include x=6 and x=2, because at these points f'(x)=0 (i.e. they are min and max respectively and not changin)
anonymous
  • anonymous
So it would be (2,6) only?
ybarrap
  • ybarrap
Yes! At all the other points, slope is positive or zero. Remember that slope is what f'(x) means: |dw:1436131100676:dw|
ybarrap
  • ybarrap
|dw:1436131184837:dw|
ybarrap
  • ybarrap
I've been forgetting to put my " ' " in my picture for f'(x) (derivative)
anonymous
  • anonymous
Alright thank you so much!!
ybarrap
  • ybarrap
You're welcome!!

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